Abstract
We obtain a first order post-Minkowskian two-body effective potential whose post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann potential. Post-Minkowskian potentials can be extracted from on-shell scattering amplitudes in a quantum field theory of scalar matter coupled to gravity. Previously, such potentials did not reproduce the Einstein-Infeld-Hoffmann potential without employing a suitable canonical transformation. In this work, we resolve this issue by obtaining a new expression for the first-order post-Minkowskian potential. This is accomplished by exploiting the reference frame dependence that arises in the scattering amplitude computation. Finally, as a check on our result, we demonstrate that our new potential gives the correct scattering angle.
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ArXiv ePrint: 2006.13234
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Grignani, G., Harmark, T., Orselli, M. et al. Fixing the non-relativistic expansion of the 1PM potential. J. High Energ. Phys. 2020, 142 (2020). https://doi.org/10.1007/JHEP12(2020)142
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DOI: https://doi.org/10.1007/JHEP12(2020)142